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\(3x + 5 < x + 11\) --> \(x<3\). So, we have that x is less than 3. There is only one prime number less than 3, namely 2. So, the question basically asks whether \(x=2\). Notice here that we are not told that x and y are integers.

(1) The sum of x and y is even. It's certainly possible that x is a prime number, for example if \(x=y=2\), but it's also possible that x is NOT a prime number, for example if \(x=y=1\). Not sufficient.

(2) The product of x and y is odd. The same here: it's possible that x is a prime number, for example if \(x=2\) and \(y=0.5\), but it's also possible that x is NOT a prime number, for example if \(x=y=1\). Not sufficient.

(1)+(2) Suppose \(x=2=prime\), then from (1) it follows that \(y=even\), but in this case \(xy=even\), not odd as stated in (2). Thus our assumption that \(x=2=prime\) was wrong. Therefore, x cannot be a prime number. Sufficient.

(2) The product of x and y is odd.INSUFFICIENT: We dont know whether y is integere.g. x=2, y=1.5 then xy=3 (ODD)e.g. x=1, y=3 then xy=3 (ODD)x can be 1 or 2, hence its not sufficient.

Combining (1) & (2)SUFFICIENT:If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN.If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODDThus if x=2, both statements cannot be true simultaneously.This information is SUFFICIENT to prove x cannot be 2.

Hence choice(C) is the answer.

According to my knowledge 1 is Neither Prime nor Composite.Please correct me if GMAT thinks the other way.I am really concerned about this

GMAT doe not have some kind of their own math.

Facts about primes:1. 1 is not a prime, since it only has one divisor, namely 1.2. Only positive numbers can be primes.3. There are infinitely many prime numbers.4. the only even prime number is 2. Also 2 is the smallest prime.5. All prime numbers except 2 and 5 end in 1, 3, 7 or 9.